1. Technical Field
The invention relates generally to floating structures used in conducting offshore petroleum operations, e.g., drilling, exploration, production, and storage. More specifically, the invention relates to an apparatus and method for controlling tension levels in tensile elements, e.g., mooring lines, marine tendons, and risers, which extend between a floating structure and the seafloor or other body.
2. Background Art
The oil industry is increasingly relying upon offshore oil deposits to meet the needs of the energy market. However, offshore operations, such as exploration, drilling, and production, are subject to a host of challenges that do not exist on dry land. These challenges become even more acute in deep water where floating structures, which are subject to irregular motions during operation, are employed. As illustrated in FIG. 1, a floating structure that is stationed in an open sea environment is subject to environmental forces of wind, waves, and current which may combine to induce the generally undesirable response of oscillatory motions along six degrees of freedom. Generally, displacements in the vertical, longitudinal, and transverse directions are referred to as heave, surge, and sway, respectively. Rotations about the heave, surge, and sway axes are generally referred to as yaw, roll, and pitch, respectively. For floating structures that are generally symmetric, the term lateral offset or surge may be used to refer to surge or sway motion of the floating structure and the term pitch may be used to refer to pitch or roll motion of the floating structure.
Frequently, it is desirable for a floating structure to remain relatively stationary either in relation to a fixed point on the seafloor or relative to another body. Holding a floating structure in position, or on station, and reducing lateral excursions about this station against the forces of the environment is referred to as station-keeping. Station-keeping is difficult in any offshore operation, especially when relatively rigid fluid-carrying pipes such as risers extend between the floating structure and the seafloor. In operations involving risers, stringent requirements are usually imposed on the station-keeping system to prevent damage to the risers. It is usually desirable to maintain tension in a riser to prevent the riser from buckling or collapsing under its own weight or under the action of the environmental forces. Thus, as the floating structure responds to the environmental forces, one of the challenges then becomes keeping the floating structure on station while providing appropriate tensile support to the riser. Various prior art structures have been developed to compensate for the motions of the floating structure while providing tensile support to risers. Deep water operations, however, have pushed the limits of traditional systems employed for riser tensioning and station-keeping. Nevertheless, the discovery of large, deep water oil deposits and the forces of economics continue to drive the industry into increasingly deeper water, thus making it desirable to have a station-keeping system and a riser tensioning system that is effective in even deep water.
Floating structures typically employ dynamic positioning systems or a system of tensile elements attached between the floating structure and the seafloor for station-keeping. Dynamic positioning systems use active means of monitoring position combined with thruster control to hold a fixed position. However, the use of dynamic positioning systems are generally limited to short term operations, such as drilling. For long term operations, floating structures generally employ tensile elements, such as mooring lines and marine tendons. Mooring lines are the most common tensile elements employed for station-keeping. Some floating structures use both mooring lines and marine tendons for station-keeping. Mooring lines are typically made of sections of chain, wire rope, synthetic rope, or a combination of such materials. In harbors, ropes are typically used to attach a floating structure to a dock or to hold station in open water. In open seas, catenary mooring lines are commonly used. Marine tendons are typically vertical, relatively rigid pipes that extend between the floating structure and the seafloor.
FIG. 2 illustrates a floating structure 10 which employs a catenary mooring system, e.g., catenary mooring line 12, for station-keeping. The catenary mooring line 12 has one end attached to the floating structure 10 and another end attached to an anchor 14 on the seafloor. Typically, the length of a catenary mooring line is significantly in excess of the depth of water in which the floating structure is moored so that the mooring line forms a characteristic sagging or catenary shape between the floating structure and the seafloor. The length of the mooring line often exceeds the water depth by a factor of three to five. The mooring line 12 connects to the floating structure 10 at a connection angle .phi., where .phi. is measured with respect to the vertical axis of the floating structure 10. The larger the connection angle .phi., the more effective is the mooring line 12 in restraining surge motions of the floating structure 10. However, the connection angle for a catenary mooring line is relatively low, typically less than forty-five degrees.
The connection angle .phi. of a catenary mooring line may be made larger by increasing the pre-tension in the mooring line or by adding buoys to the mooring line. The mooring line 18 indicates the new position of the mooring line 12 when pre-tension in the mooring line 12 is increased. The mooring line 22 indicates the new position of the mooring line 12 when buoys 20 are added to the mooring line 12. As shown, increasing the pre-tension in the mooring line 12 or adding buoys to the mooring line 12 shifts the mooring line 12 upward, thereby increasing the connection angle of the mooring line. However, as water depth increases, the connection angle of the catenary mooring line tends to diminish due to the increasing weight of the catenary mooring line, making the catenary mooring line less desirable in very deep water. The catenary mooring line may be replaced with a taut mooring line which has a much shorter length and weighs less than the catenary mooring line. FIG. 2 shows a taut mooring line 24 having one end connected to the floating structure 10 and another end connected to a pile 26 on the seafloor. The taut mooring line 24 is pre-tensioned to achieve a desired connection angle with the floating structure 10. The connection angle of the taut mooring line is generally larger than the connection angle .phi. of the catenary mooring line, allowing the taut mooring system to provide better station-keeping characteristics. A taut mooring system, however, requires substantially higher pre-tensioning than a catenary mooring system.
In both taut and catenary mooring systems, the weight of the mooring line and the geometry of the mooring system configuration combine to give a generally non-linear relationship between tensions in the mooring line and lateral offsets of the floating structure. FIG. 3 shows an example of a mooring line tension versus lateral offset curve. As shown, mooring line tension increases gradually through an initial range of lateral offsets, but beyond the initial range of lateral offsets, mooring line tension increases exponentially. As a result of this non-linear behavior, relatively small lateral offsets result in large tension variations in the mooring line in the region where mooring line tension increases exponentially. For example, a lateral offset .differential.X.sub.0-1 for a mooring line with a pre-tension To induces a tension variation .differential.T.sub.0-1. Often, it is desirable to have a highly pre-tensioned mooring line, since this will enhance the restoring response of the mooring system. This is especially true for a taut mooring system. However, a much higher pre-tension induces a much higher tension variation in the mooring line. For example, for a mooring line with a higher pre-tension T.sub.2, a lateral offset .differential.X.sub.2-3 induces a tension variation of .differential.T.sub.2-3. As shown, .differential.T.sub.2-3 is much larger than .differential.T.sub.0-1, even though the lateral offsets .differential.X.sub.2-3 and .differential.X.sub.0-1 are equal in magnitude.
Large cyclic tension variation, also known as loading cycle, during lateral oscillations of the floating structure result in increased fatigue in the mooring line and the possibility of the tension in the mooring line exceeding the breaking strength of the mooring line. Although, mooring line fatigue may also result from the forces of the waves and current inducing transverse mooring line vibrations, due to a phenomenon known as vortex shedding, the primary fatigue mode in a mooring line is due to cyclic axial tension. Thus, in designing a mooring line, several factors come into play, including design line tension, the magnitude of variations in axial tension in the mooring line during a loading cycle, and the number of loading cycles that the mooring line endures. Design line tension is the maximum expected tension that the mooring line must be able to endure without failure. For short term operations, the mooring line is usually selected such that the breaking strength of the mooring line is greater than or equal to the sum of the maximum expected tension and a factor of safety. However, over time, fatigue generally reduces the breaking strength of the mooring line. Therefore, for long term operations, the mooring line is usually selected such that the breaking strength of the mooring line is greater than or equal to the sum of the maximum expected tension, a factor of safety, and an additional factor accounting for the expected fatigue reduction in breaking strength.
Mooring lines are under constantly varying axial tension throughout their service life. Generally speaking, the smaller the magnitude of tension variations and the fewer the loading cycles, the less fatigue in the mooring line. Less fatigue allows longer service life for a mooring line with a given design line tension, or where there is a fixed service life, less fatigue allows the use of a mooring line with a smaller cross-sectional area, resulting in generally cheaper cost per unit length for the same design line tension. As water depth increases, the pre-tension required to maintain acceptable station-keeping characteristics generally increases. An increase in pre-tension generally leads to a higher maximum expected mooring line tension and higher cyclic tension variations with a commensurate increase in mooring line fatigue. The typical approach to overcoming this increased fatigue and higher maximum expected tension in the mooring line has been to increase the cross-sectional area of the mooring line. For deep water operations, this practice has led to very large and heavy mooring lines. The increase in size and weight of the mooring lines not only increases the cost of the mooring lines themselves, but also increases the cost of the mooring line handling equipment, adds expensive deck payloads, and requires the floating structure to have larger storage facilities. For example, under the current state of art, in water depths approaching four thousand feet, the diameter of a spiral metal strand mooring line may exceed six inches. The entire cost of the mooring line may constitute as much as thirty percent of the total cost of a typical drilling structure. Therefore, it would be highly desirable and economical to have a mooring system with highly pre-tensioned mooring lines but relatively low maximum line tensions and relatively small cyclic tension variations.
FIG. 4 illustrates a floating structure 30 employing a marine tendon system for station-keeping. The floating structure comprises a deck 32 that is positioned on a buoyant column 34 and pontoon structure 36. The marine tendon system includes a symmetric pattern of vertical pipes or tendons 38 hung from the floating structure 30 and rigidly connected to a tendon template 40 on the seafloor 44. The tendons 38 are pre-tensioned when the floating structure 30 is submerged to a distance .differential.Z below its free floating position and the columns 34 and pontoon structure 36 are deballasted. The tendons 38 function as rigid connections between the floating structure 30 and the seafloor 34 in the heave direction. The tendons 38 respond to heave motions of the floating structure 30 by elastically deforming along their axial axes. This tensile elastic deformation of the tendons provides a generally linear tendon tension versus heave displacement curve, with tendon tension linearly increasing with increasing heave displacement. Lateral offsets of the floating structure also induces elongation of the tendon, and a portion of the tension in the tendon, equal to the sine of the angle of the tendon with respect to the vertical, acts to provide a restoring force in the lateral direction. The shape of the tendon restoring force versus lateral offset is similar in shape to that of the mooring line tension versus lateral offset.
The applicability of a marine tendon system has primarily been limited to heave restrained vessels specifically designed to employ marine tendons. This is in part due to the complexity of marine tendon systems and the cost of installing marine tendons and tendon templates on the seafloor. The availability of highly pre-tensioned vertical tensile elements may, however, be a desirable component of the station-keeping of many floating structures for which marine tendons cannot currently be utilized. As with the design of a mooring line, the design of marine tendon systems is generally controlled by axial fatigue considerations. However, a marine tendon is basically a vertical rigid body exposed to wave and current forces near the water surface. Such forces may induce large transverse vibrations which may add additional complexity to fatigue design for marine tendons. Nonetheless, the ability to limit the maximum expected tension and magnitude of cyclic tension variations in a marine tendon would be an equally desirable feature for a marine tendon system.
Floating structures employing tensile elements for station-keeping may still encounter relatively large mean displacements and oscillations off the desired station. Heave motions of floating structures can be greatly reduced by employing marine tendon systems, but there is a substantial cost to using marine tendons and marine tendons are generally applicable to only a narrow class of specially designed vessels. It is often more economical and practical to design the hull of the floating structure to minimize heave motions. On the other hand, surge motions may be quite large under design environmental conditions, even when mooring or marine tendon systems are employed. Generally, these large surge motions occur because large amplitude second order motions for the floating structures result from resonant responses near the natural period of motion. Systems responding in resonance are critically dependent upon damping to reduce the amplitude of these motions. The hulls of floating structures, however, generally provide only a small amount of damping to the slow second-order motions. Further, the prior art tensile element station keeping systems employed also generally provide little additional damping to the floating system.
To better understand the response of a floating structure to environmental forces, a floating structure may be modeled as a spring mass system having a natural period of vibration described by the following expression: EQU T.sub.n =2.pi.M.vertline.K
where T.sub.n is the natural period of the mooring system, M is the mass of the system including added mass, and K is the stiffness of the system.
The vertical stiffness, K, in the heave direction is generally determined by the waterplane area of the submerged hull and the vertical stiffness characteristics of tensile elements, such as mooring lines and marine tendons, attached between the floating structure and another body. The horizontal stiffness, K, in the surge direction is generally determined by the horizontal stiffness characteristics of the attached tensile elements. In general, mooring lines make negligible contribution to vertical stiffness, and marine tendons make negligible contributions to horizontal stiffness. Therefore, for a moored floating structure, the stiffness in the heave direction is generally determined by the waterplane area, unless marine tendons are also employed. In the surge direction, the stiffness is generally determined by the horizontal stiffness characteristics of any attached mooring lines, independent of the use of marine tendons.
The stiffness characteristic, K, of a particular system of tensile elements is influenced by a number of factors. One important factor is the angle at which the tensile element connects to the floating structure. Generally, the closer a connection angle of a tensile element is to parallel with a particular direction of displacement, the larger the portion of tension in the tensile element that will act to reduce movement in that direction, thereby increasing stiffness, K, in that direction. Another important factor is the amount of pre-tension applied to the tensile element. For tensile elements having non-linear tension versus displacement curves, such as is typical in mooring lines, as pre-tension increases, the change in tension for a given displacement in a particular direction of displacement increases, resulting in an increase in the stiffness, K, in that direction.
The mass, M, of a floating structure is typically extremely large in comparison to the stiffness characteristics, K, of the attached tensile elements. Such a system may be referred to as an inertially controlled system. As described above, marine tendons are employed directly parallel to the direction of heave motion. Mooring lines, however, have connection angles much less than the ninety degrees required to come parallel to the direction of surge motions. The connection angles of mooring lines are typically near or below forty-five degrees. The connection angle where tendons are employed to reduce surge motions is much lower still, typically less than five degrees at the maximum expected lateral offset. Therefore, as a general rule, the vertical stiffness characteristic of the system is significantly higher than the horizontal stiffness characteristic. Vertical stiffness is also augmented by the restoring force provided by the change in buoyancy of the hull as the floating structure heaves. Thus, one can see, by reference to the expression above, that for a floating structure, the natural period, T.sub.n, in the heave direction is generally much shorter than the natural period, T.sub.n, in the surge direction. By way of example, a typical floating structure employing marine tendons, e.g., Tension Leg platform, may have a heave natural period of three to five seconds while a floating structure not employing marine tendons, e.g., SPAR platform or semi-submersible, may have a heave natural period of twenty-five to thirty seconds. The surge natural period of a typical floating structure, however, may be on the order of one hundred to three hundred seconds.
When a floating structure is stationed in an open sea environment, the floating structure is exposed to the forces of wind, current, and waves. Wind and current may be generally steady for time scales on the order of the natural period of an offshore structure, thereby generally inducing a non-oscillating, or mean, offset. However, wave patterns are generally irregular on these time scales and generally induce an offset having both a mean portion and an oscillating portion. An irregular wave surface is characterized by the presence of a large number of individual waves with different wave periods and wave heights. The statistical properties of such a surface may be described by means of a wave energy spectrum or wave energy distribution such as illustrated in FIG. SA. The motion response of the floating structure may be characterized by means of a Response Amplitude Operator (RAO) such as illustrated in FIG. 5B.
The expected motion response of the floating structure may be derived from the product of the wave energy spectrum and the square of the Response Amplitude Operator, as illustrated in FIG. 5C. For example, the primary wave period for a one hundred year hurricane condition in the Gulf of Mexico is between fourteen and sixteen seconds. This environmental condition is often used as a design condition environment for floating structures employed in the Gulf of Mexico. The surge natural period of a typical moored floating structure employed in the Gulf of Mexico for production operations is on the order of one hundred to three hundred seconds. As can be appreciated by reference to FIGS. SA to 5C, the surge motion response spectrum may be a double peaked curve. The first peak, which represents the first order motions occurring near the primary wave period, may be significantly smaller than the second peak, which represents the second order motions occurring near the surge natural period of the floating structure. A relatively small input of wave energy, generally corresponding to a relatively small magnitude of environmental forces, may induce large resonant response surge motions.
As illustrated in FIG. 6, the expected motion response of a floating structure in real-time may be broken down into three constituent components: a steady state offset, first order oscillations near the primary wave period, T.sub.peak, and second order oscillations near the natural period, T.sub.natural, of the floating structure. Steady state motions are induced by mean portions of the environmental forces, e.g., mean potential drift, mean wind drift, mean viscous drift, and mean current drift. In the surge direction, these environmental forces combine to induce a mean lateral offset, L.sub.mean, called the static offset. Second order motions, called second order oscillations, occur as slow oscillations about the mean lateral offset, L.sub.mean. First order motions, called first order oscillations, occur as superimposed oscillations over the second order oscillations to trace out the actual position of the floating structure through time. As illustrated in FIG. 6, all environmental forces are assumed to be applied in phase and in the same direction, thereby resulting in a maximum expected lateral offset, L.sub.mean. This maximum expected lateral offset, L.sub.max, generally represents the extreme condition used for tensile element design. Often an absolute limit is placed on the maximum expected lateral offset, L.sub.max, to prevent damage to the risers. Large lateral offsets also add challenges to riser tensioning systems just as with large heave motions. It is, therefore, desirable to minimize the maximum lateral offset.
The primary function of a mooring or marine tendon system is to reduce mean portions of the motions of a floating structure. The magnitude of the mean portions of the motions may generally be reduced by increasing the pre-tension in the tensile elements used in a station-keeping system, i.e., by increasing the system stiffness. Generally, however, a mooring or marine tendon system has little effect in reducing dynamic motions due to the huge inertial force of the floating structure. Despite an increase in the pre-tension in the tensile element, the magnitude of the dynamic oscillations may not be significantly reduced. Little attention is generally paid to the first order motions because they are generally small relative to the mean offset and second order motions. As described above, the second order lateral oscillations of floating structures, however, are resonant motion responses and may be very large for a small input of environmental forces. The response amplitude of a resonant system is critically dependent upon the damping of the system, rather than the system stiffness, but the system damping characteristic for the second order motions is generally low for floating structures. This characteristic is due to the very slow velocity at which second order motions occur because of the large lateral natural periods. Wave damping acts to reduce shorter period motions by opposing rapid changes in velocity, such as heave motions and first order surge motions, but wave damping has little effect on the slow second order surge oscillations involving slow changes in velocity. Damping to reduce these second order resonant motions must be provided from other sources, such as the tensile element systems. Generally, increased damping results in lower amplitude resonant motion response. It is, therefore, generally desirable to have highly damped station keeping system to reduce surge motions of floating structures.
Now returning back to riser tensioning systems, an effective riser tensioning system should be able to maintain tension throughout the entire length of the riser to avoid any compressive loads in the riser. This is because risers are typically not designed to withstand compressive loads and such loads would generally result in buckling of the riser. Conventionally, the tensile force applied to a riser is between 1.2 and 1.8 times the riser load. The lower limit is generally set by the requirement to provide sufficient vertical force to keep the length of the riser in steady tension. The lower limit of the tensile force may also be affected by fatigue concerns due to transverse vibrations induced by the action of current and waves. As a general rule, the higher the tensile force applied, the smaller the amplitude of transverse riser pipe vibration from current and waves. The practical upper limit for the tensile force applied to the riser is determined by the tensile capacity of the riser. However, traditionally, it has been cost prohibitive to employ riser tensioning systems capable of employing the full tensile capacity of the risers.
An effective riser tensioning system should also be able to apply constant tensile force to the riser through a large of relative displacements between the top of the riser and the vessel. A certain limited range of variation in tensile loading may be acceptable to provide the desired service life of the riser. However, varying tensile forces induce fluctuations in the tensile stress levels in the riser. Even though the tensile force levels may be low, it is the variable application of these loads which shorten the life span of the riser through fatigue. The task of providing constant tension for risers, especially through a large range of relative displacement between the top of the riser and the vessel, has presented a significant obstacle to deep water operations.
Riser tensioning systems may be active, passive, or a combination of both. Active systems using pneumatic, hydraulic, cable, and sheave systems to support the weight of the riser are widely used. However, active systems require a substantially continuous input of energy and monitoring. Further, a battery of auxiliary equipment is required to supply fluids necessary for operations. Still further, active systems are subject to chronic maintenance and failure, requiring redundancy in the system to permit down time of an individual unit for replacement or repair. Passive systems on the other hand require little or no external input to function and virtually no monitoring. Accordingly, it would be desirable to provide a passive riser tensioning system. Further, a desirable riser tensioning system would be substantially maintenance free and would not have expected failures during the design service life.
There are various prior art passive tensioning systems. One prior art passive system supports a portion or all of the weight of the riser through use of buoyancy elements, e.g., buoyancy tanks filled with syntactic foam modules or buoyancy cans filled with ballast elements, attached to the riser below the water surface. The buoyancy cans may be attached to the riser near the water surface and deballasted by injecting high pressure air into the ballast elements. However, buoyancy cans may induce interference problems between the various risers, and so must be shielded from wave, current, and other forces which might cause movement of the cans. Buoyancy tanks filled with syntactic foam modules may be attached to the risers deep beneath the water surface, where wave and current forces are less pronounced. However, because the space around the riser is often limited, the buoyancy tank may not be large enough to support all of the weight of the riser.
U.S. Pat. No. 5,366,324 to Edward Arlt discloses a passive system that uses linear deformation of springs to maintain tension in the riser. Because the reaction force of the springs increase linearly as the springs deform elastically, a mechanical lever system is typically provided to compensate for the increasing reaction force. The mechanical lever system deflects the springs to apply force to the riser at a diminishing angle as the reaction forces of the springs increase. Through a limited range of elastic deflection of the springs, the apparent angle of the roughly linearly increasing reaction force versus deflection curve is reduced in a direction parallel to the riser. This provides a lower magnitude of cyclic tension variations in the riser for a given displacement as compared to applying the force of the springs in a direction parallel to the length of the riser.
U.S. Pat. No. 5,160,219 to Edward Arlt discloses another spring-based passive system that employs a combination of variable spring rates and geometry to reduce the apparent reaction force versus deflection curve toward the goal of providing constant tension over a range of displacement. The geometry employed may be similar to that of the previously described spring-based system. This system, however, employs springs which are a combination of elastomers of various modulus of elasticity. The springs may comprise concentric portions of various elastomers bonded one inside another to form a cone-like shape. Through initial displacements, the elastomer portion having the lowest modulus of elasticity deflects linearly to an angle wherein a portion having a higher modulus of elasticity begins to deflect. This spring design further reduces the apparent reaction force versus deflection curve in a direction parallel to the riser.
These spring-based systems depend upon the linear deformation of elastomeric materials. They generally employ relatively complex mechanical apparatus, and have heretofore provided only a limited range of relative displacement and service life for the riser.
U.S. Pat. No. 4,359,095 to Riley Goldsmith discloses another passive system that uses non-linear deformation of buckling elastomer columns to maintain tension in a riser. Buckling elastomer columns are, however, subject to creep, hysteresis, lateral or rotational instability, and reaction force drop-off through the buckled range of deflection. Further, a single buckling elastomer column can provide only a limited range of deflection and magnitude of riser tension. However, the spring rate of a column in the buckled range of deflection can provide a much softer reaction force versus deflection curve, eliminating the need for a complex mechanical apparatus to limit reaction force as in the previously described spring-based systems.
A classic mechanical engineering problem involves the prediction of column buckling. Referring to FIG. 7, when a slender body, such as a column, comprised of an elastic material, is compressed axially (F.sub.0 to F.sub.1) it will deflect elastically through an initial range of deflections (.differential.X.sub.1), essentially reducing in length. The slope of this curve in the elastic deflection range is often almost linear (.differential.X/dF). At some critical point (X.sub.critical), however, the column will buckle outward and deform non-linearly. The column will then generally deflect through some range of buckled deflection (.differential.X.sub.2) before snubbing occurs (.differential.X.sub.3). As shown, the reaction force versus deflection characteristics differ substantially between the linear range of deflection (.differential.X.sub.1) and the buckled (.differential.X.sub.2) range of deflection. Many reaction force versus deflection characteristics may be designed by varying aspects such as the material properties of the column, the cross-sectional shape along the column's length, or the geometric arrangement of multiple columns. The typical curve has a decreasing reaction force past initial buckling (.differential.X.sub.2), before the force again begins to increase just prior to material failure (.differential.X.sub.3) as snubbing occurs. The shape of the curve in the buckled range is, however, subject to manipulation. Curves having a constant, slowly increasing, and slowly decreasing reaction force over a range of deflection are all possible.
In general, however, industry has found few uses for this buckled deflection characteristic of elastic materials. This may be primarily due to the fact that buckled deflection is non-recoverable in most elastic materials, such as metals. As shown in FIG. 7, a permanent, or non-recoverable, deflection (.differential.X.sub.p) will remain after unloading the column. This makes the buckled deflection either a non-repeatable process, or one that may be repeated only a limited number of times. There are classes of materials, however, that have the property of high resistance to the shear strain generally involved with buckled deflection. The full range of buckled deflection may be recoverable and repeatable for these materials. Such buckling elastic materials, or elastomers, will repeatedly return to the unbuckled and undeflected condition upon removal of the compressive force. Generally, these materials are synthetic polymers, but there are also naturally occurring buckling elastomers.
One naturally occurring elastomer is rubber. Synthetic rubber, however, is more frequently used by industry. Both natural and synthetic rubber have the property of being extremely durable against repetitive loading or fatigue, as well as being wear and corrosion resistant. Rubber also has excellent properties for resisting both compressive loads and shear loads. Further, rubber has a specific gravity of near that of seawater, making rubber roughly neutral buoyant in seawater. The offshore industry makes use of rubber products for many purposes, such as for barge bumpers, boat landings, fenders, riser guards, shock absorbers, and many other applications. The applications of rubber in the offshore industry have generally been for protection devices, utilizing the energy absorbing properties of rubber to absorb the energy of dynamic and impact loads as heavy floating objects collide. Some of these applications employ rubber configurations that take advantage of the shear resistant properties of rubber and the buckled deflection of elastomer columns.
One example is the dock fender. Dock fenders are employed to absorb the large kinetic energy of ships when they strike up against the dock sides during docking. The fenders are designed to absorb a large quantity of kinetic energy for a given deflection. An exemplary buckling elastomer column unit employed in a dock fender is illustrated in FIG. 8A. The configuration shown is typically referred to as a cell fender. As shown in the reaction force versus deflection curve, the elastomer unit of the cell fender has a steep curve through the initial linear portion curve to quickly provide a high force to oppose a heavy barge. At a critical point the fender buckles, and the reaction force curve begins to dip slowly an amount (.differential.F.sub.1). This characteristic is employed to provide a large area under the curve, representing the energy absorbed by the dock fender, for a given fender deflection (X.sub.1). The larger the area under the curve, the greater the ship impact that may occur without damage to ship or dock.
As illustrated in FIG. 8B, the quantity of energy absorbed can be increased for a given maximum force by extending the length of buckled deflection an amount (X.sub.2). One manner in which this can be achieved is by employing a configuration of elastomer columns at some angle (.phi.) off vertical, in a cone shape rather than the tubular configuration of a cell fender. As illustrated in FIG. 8C, the amount of energy absorbed can further be increased by reducing the reaction force drop-off (.differential.F.sub.2) through the buckled range of deflection. One known manner in which this can be achieved is by adjusting the cross-section of the elastomer column, such as by increasing the thickness of the column (T) in the appropriate place.
FIG. 9 illustrates one possible reaction force versus deflection curve that may be designed by a structured configuration of buckling elastomers, referred to as an elastomer spring. As can be appreciated by reference to FIG. 9, when the elastomer spring is initially subjected to compressive loading, the spring provides a roughly linearly increasing reaction force versus deformation curve (.differential.X.sub.0 /.differential.T.sub.0). However, when loading reaches a critical force (T.sub.1), the walls of the spring configuration buckle. Through a range of deformation following first buckling (.differential.X.sub.1), the buckling elastomer spring deforms non-linearly and may be designed to provide a substantially constant reaction force. This type of non-linear deformation is structural and recoverable, unlike the previously described non-recoverable variety, incident to materials such as metals and other less strain-resistant materials. As such, this type of non-linear deformation can be repeated. At the end of this range of non-linear deformation, the non-linear range is exceeded and the reaction again begins to increase with increasing deformation until failure results.
Several difficulties arise in employing elastomers for repetitive loading over a long duration. One problem can be the hysteresis characteristic of the reaction force versus deflection curve. As illustrated in FIG. 9, a buckling elastomer spring generally traces a different path on the reaction force versus deflection curve during the loading phase than it does during the unloading phase. The curve follows a path of lower reaction force during unloading. As described above, this result is due to the fact that the rubber absorbs a certain amount of energy during each cycle of loading and unloading. In a purely elastic deflection, a spring will trace the same path along the curve, essentially conserving the mechanical energy. In the case of a buckling elastomer spring, however, non-linear deformations of the elastomer are subject to a drop in reaction force when the unloading phase begins. The path traces back along a different line throughout the non-linear and linear ranges. The path traced is generally dependent upon the velocity and amplitude of deflection. However, the buckling elastomer spring will return to the original undeformed configuration at the end of the unloading cycle. In both instances, the area within the loop made by tracing the loading and unloading path, referred to as a hysteresis loop, is a measure of the quantity of heat energy absorbed during the loading and unloading cycle. The spring will heat up unless the energy can be radiated away from the spring. Elastomers such as natural rubber may be particularly subject to overheating. The shape of the reaction force versus deflection curve for a buckling elastomer spring may begin to degrade at temperatures as low as one hundred eighty degrees.